Solve (1-1/2^2)(1-1/3^2)(-1/4)

$$( 1 - \frac { 1 } { 2 ^ { 2 } } ) ( 1 - \frac { 1 } { 3 ^ { 2 } } ) ( - \frac { 1 } { 4 } )$$

Evaluate

$$-\frac{1}{6}\approx -0.166666667$$

Solution Steps

Calculate 2 to the power of 2 and get 4.

$$\left(1-\frac{1}{4}\right)\left(1-\frac{1}{3^{2}}\right)\left(-\frac{1}{4}\right)$$

Convert 1 to fraction \frac{4}{4}.

$$\left(\frac{4}{4}-\frac{1}{4}\right)\left(1-\frac{1}{3^{2}}\right)\left(-\frac{1}{4}\right)$$

Since \frac{4}{4} and \frac{1}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4-1}{4}\left(1-\frac{1}{3^{2}}\right)\left(-\frac{1}{4}\right)$$

Subtract 1 from 4 to get 3.

$$\frac{3}{4}\left(1-\frac{1}{3^{2}}\right)\left(-\frac{1}{4}\right)$$

Calculate 3 to the power of 2 and get 9.

$$\frac{3}{4}\left(1-\frac{1}{9}\right)\left(-\frac{1}{4}\right)$$

Convert 1 to fraction \frac{9}{9}.

$$\frac{3}{4}\left(\frac{9}{9}-\frac{1}{9}\right)\left(-\frac{1}{4}\right)$$

Since \frac{9}{9} and \frac{1}{9} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3}{4}\times \frac{9-1}{9}\left(-\frac{1}{4}\right)$$

Subtract 1 from 9 to get 8.

$$\frac{3}{4}\times \frac{8}{9}\left(-\frac{1}{4}\right)$$

Multiply \frac{3}{4} times \frac{8}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3\times 8}{4\times 9}\left(-\frac{1}{4}\right)$$

Do the multiplications in the fraction \frac{3\times 8}{4\times 9}.

$$\frac{24}{36}\left(-\frac{1}{4}\right)$$

Reduce the fraction \frac{24}{36} to lowest terms by extracting and canceling out 12.

$$\frac{2}{3}\left(-\frac{1}{4}\right)$$

Multiply \frac{2}{3} times -\frac{1}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2\left(-1\right)}{3\times 4}$$

Do the multiplications in the fraction \frac{2\left(-1\right)}{3\times 4}.

$$\frac{-2}{12}$$

Reduce the fraction \frac{-2}{12} to lowest terms by extracting and canceling out 2.

$$-\frac{1}{6}$$

Factor

$$-\frac{1}{6} = -0.16666666666666666$$